How Does Intracellular Ca²⁺ Oscillate: By Chance or by the Clock?

Abstract

Ca²⁺ oscillations have been considered to obey deterministic dynamics for almost two decades. We show for four cell types that Ca²⁺ oscillations are instead a sequence of random spikes. The standard deviation of the interspike intervals (ISIs) of individual spike trains is similar to the average ISI; it increases approximately linearly with the average ISI; and consecutive ISIs are uncorrelated. Decreasing the effective diffusion coefficient of free Ca²⁺ using Ca²⁺ buffers increases the average ISI and the standard deviation in agreement with the idea that individual spikes are caused by random wave nucleation. Array-enhanced coherence resonance leads to regular Ca²⁺ oscillations with small standard deviation of ISIs.

INTRODUCTION

How are random molecular events orchestrated into reliable cellular behavior like global intracellular Ca²⁺ oscillations? If many molecules are involved, it is generally assumed that the cell behaves like a continuously stirred reactor and the law of large numbers establishes predictable behavior (1). Most models of the dynamics of intracellular Ca²⁺ release adopt this idea (2–4), but it is not consistent with experimental analyses showing that global oscillations arise from Ca²⁺ waves initiated locally (5–9). Such a local mechanism is predicted to lead to stochastic oscillations because although each cell has many IP₃Rs and Ca²⁺ ions, the law of large numbers does not apply to the initiating event (3,10), which is restricted to very few IP₃Rs by steep Ca²⁺ concentration gradients (7,9,11). Indeed, the law of large numbers may not apply either to other signaling pathways that generate steep intracellular concentration gradients (12).

Oscillations of intracellular Ca²⁺ dynamics exhibit spike trains which appear rather regular by casual inspection. This led to formulation of models with an oscillatory deterministic regime (2–4), but cells might exhibit stochastic dynamics which produce very similar global signals. That type of dynamics, often described as a stochastic medium (10,13–16), was predicted theoretically for reaction-diffusion systems with discrete stochastic sources of the diffusing species. Intracellular Ca²⁺ dynamics may be perceived as a stochastic medium: the diffusing species is cytosolic Ca²⁺ and the discrete stochastic sources are ion channels. Such systems generate spatiotemporal structures by wave nucleation due to thermal noise. In general, that leads to random spike sequences. The randomness does not arise from small numbers of molecules in the system, but rather from the fact that global events are initiated locally. Stochastic media exhibit almost regular oscillations in the regime of array enhanced coherence resonance (AECR) (10,13–16). Herein wave initiation is frequent enough to ensure that waves emerge as soon as the refractory period has passed. While there is experimental and theoretical evidence for the nucleation of global Ca²⁺ release events by local events (7,9,10), we investigate here whether spike sequences are random.

Transient changes in cytosolic Ca²⁺ concentration are used with great versatility to signal within cells (17). Under appropriate conditions and in many cell types, these transients form oscillations that encompass the entire cell (6,7,9,17). The interspike interval (ISI) of these oscillations varies from a few seconds to many minutes and their temporal profiles include spikes, sinusoidal oscillations, and bursts (2,3,7).

In many cells, including those examined in this study, oscillatory changes in free cytosolic Ca²⁺ concentration ([Ca²⁺]_i) result from the periodic release of Ca²⁺ from intracellular stores within the endoplasmic reticulum (ER). Release of Ca²⁺ occurs via intracellular Ca²⁺ channels, notably inositol 1,4,5-trisphosphate receptors (IP₃Rs), and Ca²⁺ is then resequestered into the ER by Ca²⁺ pumps (SR/ER Ca²⁺-ATPases). IP₃Rs are regulated by the Ca²⁺ they conduct, such that fast activation by cytosolic Ca²⁺ and slower inhibition lead to a bell-shaped Ca²⁺-dependence of the stationary open probability of the IP₃R (18–20). Within the membrane of the ER, clusters of IP₃Rs are separated by perhaps 1–7 μm (8,9,21), and clustering is also dynamically regulated (22,23). These clusters of channels generate global concentration spikes via a hierarchy of Ca²⁺ release events (5–7) that depend upon Ca²⁺ diffusing between IP₃Rs to ignite the activity of successive clusters (3,17). The smallest Ca²⁺ release events, blips (5), probably reflect random openings of single IP₃Rs . Larger events, puffs, lasting tens of milliseconds and restricted to a volume of <0.5 fl, reflect the almost simultaneous opening of a few IP₃Rs within a cluster (5,8,9,21). Many coordinated puffs form oscillations and waves (3,24,25). Ca²⁺ oscillations therefore depend upon both the spatial organization of IP₃Rs and their regulation by Ca²⁺ (19,20,26).

The links between IP₃R behavior and Ca²⁺ oscillations are poorly understood. Is oscillatory behavior a feature of individual IP₃Rs and their local interaction with Ca²⁺ and IP₃, with channels opening and closing in oscillatory fashion? Or do oscillations arise from properties that depend upon a higher level of organization involving many IP₃Rs? Is AECR the new quality added by the more complex organization that would allow oscillations to emerge even from nonoscillatory elements?

With oscillatory dynamics arising from local interactions between individual IP₃Rs and their ligands, each IP₃R cluster is also an oscillator because channels within a cluster are synchronized by Ca²⁺ diffusion (11). Characteristics of the global oscillation, like period and amplitude, would be determined by local parameters such as channel state dynamics. Spatial coupling of channel clusters by Ca²⁺ diffusion would serve only to synchronize the oscillations. The global oscillation is deterministic: it has regular ISI and the timing of each spike is predictable. But recent theoretical studies suggest that IP₃R clusters are not deterministic oscillators (10,27). A deterministic model generates oscillations only if IP₃Rs are exposed to Ca²⁺ concentrations similar to those that cause their half-maximal regulation (∼0.1–10 μM) (18–20,26). Local Ca²⁺ concentrations near open IP₃Rs are much higher, and therefore do not allow for deterministic oscillations (11,27–29).

Another possibility is that stochastic fluctuations render IP₃R clusters oscillatory. Stochastic behavior of IP₃R clusters is observed experimentally as Ca²⁺ puffs (6,9). Simulations show that random binding and dissociation of Ca²⁺ and IP₃ to IP₃Rs are sufficient sources of stochastic fluctuations to explain the random generation of Ca²⁺ puffs (10,30,31). However, these fluctuations alone cannot generate the observed timescale of global oscillations because puff durations and frequencies are 3–100 times faster than the ISI in cells (6). Processes occurring within a single IP₃R cluster do not, therefore, transform random molecular behavior into oscillations. Local processes are not oscillatory, and so the idea that channel clusters are oscillators is untenable. A higher level of spatial organization is required to generate oscillations. The next spatial level is the cell, with its array of IP₃R clusters each capable of generating Ca²⁺ puffs.

That suggests that intracellular Ca²⁺ dynamics behave as a stochastic medium. Experimental and theoretical studies show that Ca²⁺ puffs can initiate global Ca²⁺ spikes (3,6,7,9,10). But theoretical analysis suggests that cells would not then oscillate deterministically; instead, they would produce random sequences of global Ca²⁺ release events (3,10,27,32). In particular, factors that modify spatial coupling would affect both frequency and the ability to oscillate (3,10).

METHODS

Measurements of [Ca²⁺]_i in glia

Glial cell cultures were prepared from brains of newborn NMRI mice (33) using whole brains for microglia, but only cortex for astrocyte cultures. Cells were loaded with fluo4-AM (5 μM) for 30 min at 20°C in glial medium (148.9 mM NaCl, 5.4 mM KCl, 1 mM MgCl₂, 10 mM CaCl₂, 5 mM HEPES, and 10 mM D-glucose, at pH 7.4). Cultures were fixed within the microscope chamber by a U-shaped Pt wire and superfused with glial medium at 20°C. Cells were illuminated (495 nm) from a monochromator (TILL Photonics, München, Germany) and fluorescent images (515–545 nm) collected every 3 s with a 12-bit camera (SensiCam, Cooke, Romulus, MI) on an upright microscope and visualized with ImagingCellsEasily software (Max Dulbrück Center, Berlin, Germany).

Measurements of [Ca²⁺]_i in human embryonic kidney (HEK) cells

HEK293 cells were cultured in Dulbecco's modified Eagle's medium/Ham's F-12 supplemented with fetal bovine serum (10 %) and L-glutamine (2 mM), in a humidified atmosphere (95% air, 5% CO₂, 37°C). Medium was replaced every third day, and cells were passaged when they reached 80% confluence. For single cell imaging, cells were plated onto 22-mm round glass coverslips coated with 0.01% poly-L-lysine and used after two days. They were loaded with 2 μM Fura-2-AM in HEK medium (135 mM NaCl, 5.9 mM KCl, 1.2 mM MgCl₂, 1.5 mM CaCl₂, 11.6 mM HEPES, 11.5 mM D-glucose, and pH 7.3) supplemented with 1 mg/ml bovine serum albumin and 0.02% Pluronic F-127. Cells were loaded for 45 min at 20°C and then washed for 45 min in HEK medium to allow deesterification of the Fura-2-AM. Measurements of [Ca²⁺]_i in single cells were performed as previously described (34), with fluorescence collected at intervals of 5 s. Fluorescence ratios were calculated after correction for autofluorescence.

Measurements of [Ca²⁺]_i in processed lipoaspirate (PLA) cells

The study conforms to the Declaration of Helsinki and all cell donors gave their informed written consent to use part of their fat tissue for the generation of processed lipoaspirate (PLA) cells.

PLA cells were isolated from fat tissue (35) and cultured in 25 cm² flasks in 5% CO₂, humidified air at 37°C in Ham's F-10 medium (Biochrom, Berlin, Germany) supplemented with 10% fetal calf serum (Sigma, St. Louis, MO), 2 mM glutamine, 0.1 mM β-mercaptoethanol, 1–100 nonessential amino acids (Biochrom), 100 units/ml penicillin and 100 μg/ml streptomycin (Invitrogen, Carlsbad, CA). Subconfluent cell cultures were dissociated with a 0.2% trypsin-0.05% EDTA solution and subcultured onto 12 mm coverslips. For Ca²⁺ measurements, subconfluent cells on coverslips were incubated for 30 min with 10 μM fluo3-AM (Invitrogen) and then washed once in culture medium. Fluo-3 fluorescence was recorded in single cells by confocal laser-scanning microscopy (laser scanning microscope model No. 510 Meta; Zeiss, Jena, Germany) using a 25× objective with a numerical aperture of 0.8 (Plan Neofluor; Zeiss). Excitation was at 488 nm and emission was recorded using a 515 nm longpass filter.

DATA ANALYSIS

All fluorescence signals, whether derived from single wavelength or ratiometric indicators, are expressed relative to the baseline fluorescence (ΔF = signal/basal). Because we analyze only interspike intervals (ISIs), there is no need to calibrate ΔF to [Ca²⁺]_i. For each single-cell time series of fluorescence, the time points of the maxima above a minimal level were determined resulting in a series of spike times, which was used to determine the ISIs. The calculations of statistical characteristics require a stationary ISI series. However, most experimental records of HEK cells have a slight trend and eventually stop oscillating. We reduced that trend by leaving out parts of the ISI series in the beginning and end showing very obvious trends and removed linear trend from the remaining series before we calculated the average period T_av, the standard deviation σ, and correlations. This is illustrated in Supplementary Material Fig. S7.

Correlation coefficients ρ_k between an ISI and its k^th successor for the l^th ISI-series were calculated according to

(1)

With the we formed the population average across n cells by

T_av-σ relation for time-dependent global nucleation rate

We show that a global nucleation probability increasing by a relaxation to an asymptotic value provides T_av-σ relations compatible with our findings. We choose a time-dependent nucleation rate Λ like

(2)

with the regeneration rate ξ. The value ξ could describe, e.g., the recovery from inhibition (36). The probability of observing a global wave at time t is given by

(3)

With this expression we can calculate the first two moments as

(4)

(5)

That can be integrated by parts,

(6)

where the first term vanishes, leading to

(7)

for T_av. 〈T²〉 is given by

(8)

Integration yields

(9)

(10)

where Γ(x) denotes the Euler Γ-function, Γ(x, y) the incomplete γ-function, and F[x] is the generalized hypergeometric function ₂F₂(x). With the relation for the standard deviation

(11)

we obtain the T_av-σ relations shown in Fig. 1.

FIGURE 1.

T_av-σ relation resulting from Eqs. 7 and 8. The lines ξ = constant arise by varying λ. They start at (0,0) with λ = ∞ and converge to T_av = σ with increasing ξ. The lines λ = constant start on T_av = σ = λ⁻¹ with ξ ≫ λ very large. Note that the T_av-σ relation becomes linear for λ/ξ → 0 or T_av → ∞ and σ → ∞ and that the slope decreases from one for ξ → 0. The values ξ and λ are measured in s⁻¹.

We did not consider a deterministic part T_d of the ISI in the above calculations, which represents an absolute refractory part of the ISI. Such a deterministic part simply moves the curves in Fig. 1 to larger values of T_av. The complete distribution including T_d is

(12)

The analysis of experimental data showed that T_av, σ, and T_d vary between individual cells of the same cell type.

RESULTS AND DISCUSSION

To establish whether intracellular Ca²⁺ oscillations are deterministic or stochastic, we performed comprehensive measurements of ISI series in different cell types. In each case, IP₃Rs evoke the Ca²⁺ oscillations (37–39) (Fig. S8). Fig. 2 shows representative time series of global oscillations in astrocytes, microglia, PLA stem cells from human adipose tissue, and human embryonic kidney (HEK) cells. These examples show that ISIs are not regular. The length of the ISI changes randomly. Records like these were used to determine the serial correlation coefficients ρ_k, mean values T_av, and standard deviations σ of ISI. For all cell types and with all degrees of stimulation, σ increases with T_av (Fig. 3).

FIGURE 2.

IP₃-mediated Ca²⁺ spikes in diverse cells. Representative examples of oscillation time series for astrocytes (A), microglia (B), PLA cells (C), and HEK cells stimulated with 30 μM carbamyl choline (CCh) (D). The oscillations in panels A–C are spontaneous. Changes in the fluorescence of the Ca²⁺ indicator relative to its basal level (ΔF) report the increase in free cytosolic [ Ca²⁺ ]. Lower panels show the ISI after each spike, with ISI defined as the interval between consecutive fluorescence maxima.

FIGURE 3.

Ca²⁺ spikes occur randomly. Dependence of the standard deviation σ of ISI on the average ISI T_av for 366 astrocytes (A), 224 microglia (B), 270 PLA cells (C), and 137 HEK cells stimulated with 30 μM CCh (D). σ and T_av were obtained from time series of single cells by temporal averaging. The correlation coefficient ρ shows that σ and T_av are highly correlated in all four cases.

Standard deviations are of the same order of magnitude as averages for most points, and for large T_av, σ and T_av are similar. Hence, the uncertainty in predicting the occurrence of a spike is of the same order as the mean ISI: i.e., Ca²⁺ spikes are random events. If spikes represented the active phase in a deterministic oscillation, the standard deviation of ISI would instead be in the range of the global interpuff interval, i.e., between a few hundred milliseconds for short T_av and a few seconds for long T_av. The uncertainty in spike timing shows in the correlation coefficients ρ_k of the ISI time series between the i^th and (i + k)^th ISI (Fig. 4). Consecutive intervals are not correlated, confirming the randomness of the spike-generating mechanism.

FIGURE 4.

Successive ISI are not correlated. Correlation coefficient ρ_k between the i^th and (i+k)^th ISI averaged across n time series obtained in the experiments shown in Fig. 6 before (red) and after (blue) loading with additional Ca²⁺ buffer. The protocols are shown in the insets (see also caption of Fig. 6). The number of time series measured for the first and the second periods were, respectively: (A) n₁ = 27, n₂ = 20; (B) n₁ = 35, n₂ = 18; (C) n₁ = 36, n₂ = 35; (D) n₁ = 33, n₂ = 23; (E) n₁ = 35, n₂ = 35; (F) n₁ = 35, n₂ = 28; (G) n₁ = 31, n₂ = 22; and (H) n₁ = 29, n₂ = 18. Error bars show standard error for averaging over n time series.

We conclude that global oscillations result from a sequence of randomly occurring global Ca²⁺ spikes. The data show also that σ almost vanishes at the smallest values of T_av, indicating that almost regular oscillations with ISIs close to T_d do exist. The results are similar for spontaneous oscillations in astrocytes, microglia, and PLA cells, and for oscillations evoked by different levels of stimulation in HEK cells, suggesting that IP₃-evoked Ca²⁺ oscillations are sequences of stochastic spikes in many cell types.

Our conclusion is compatible with the idea that each Ca²⁺ spike reflects the passage of a Ca²⁺ wave across the cell driven by successive activation of IP₃R clusters by Ca²⁺ diffusing between them (6,7,9). This mechanism can generate the spectrum of observed shapes of oscillations (3,10). Our results show that waves initiate randomly. The time of initiation is not set by a deterministic process, such as recovery from Ca²⁺-inhibition or a progressive sensitization of IP₃Rs by Ca²⁺.

Stochastic models of repetitive waves show that if σ is of the same order as T_av, it is dominated by the probability (P_trig) of triggering a wave after the cell has recovered from the previous one (10). The smaller the value of P_trig, the longer it takes on average for the next wave to occur, and the larger is the value of σ. For such repetitive triggering of waves, σ increases linearly with T_av, and σ = 1/P_trig holds for large values of T_av. Even if P_trig relaxes exponentially from 0 immediately after a spike to an asymptote, the linear relation between σ and T_av for large T_av still holds and it has a slope <1 (see Fig. 1 and Fig. 3 D). Such a relaxation of P_trig appears to apply also to wave initiation reported in Marchant and Parker (9). Almost regular oscillations arise when P_trig is very large, because then as soon as the cell has recovered from one spike, the next one is triggered. We refer to the length of the ISI of these regular oscillations as the deterministic part T_d of the ISI. It might be set by a variety of processes depending on cell type, for example: store refilling, IP₃R inhibition, or Ca²⁺-feedback to the IP₃ concentration. Each of these processes may also cause a time-dependence of P_trig such as that described in a simplified way by the relaxation with time constant ξ in Eq. 2.

The time-dependence of the global nucleation rate differs between the different cell types as revealed by the slopes of the relationship between σ and T_av. Fig. 5 shows values of the parameters of the time-dependent global nucleation rate (Eq. 2) for the different cell types. The spontaneous oscillations in astrocytes and microglia have a slope of the σ-T_av-relation close to 1 and an asymptotic nucleation rate λ much smaller than the relaxation rate ξ. Despite the relatively fast recovery from the previous spike, these oscillations are neither fast nor regular, since the asymptotic nucleation rate λ of these cells is small. The stimulated oscillations in HEK cells show the inverse relation between λ and ξ. That is correlated with the information content of stimulated and spontaneous oscillations which increases with increasing λ/ξ (40).

FIGURE 5.

Values of the parameters λ and ξ of the time-dependent global nucleation rate Eq. 2 for the different cell types. The values were obtained by fitting σ and T_av of individual time series to Eqs. 10 and 11 to obtain λ and ξ, which were then averaged across all cells of the same type. We have approximated T_d by the smallest value of T_av observed for the corresponding cell type in the fitting procedure. Error bars show standard error.

Recovery from the previous spike is relatively slow in HEK cells. That corresponds to the initial decline in spike amplitudes in Fig. 2 during which the cell reaches a state corresponding to incomplete recovery from a spike during each ISI. One possibility is that insufficient refilling of the ER causes the decline. We might then suggest that immediately after stimulation, Ca²⁺ reuptake during the ISI fails to keep pace with release during a spike and successive Ca²⁺ transients decrease in amplitude. But during the stationary phase of oscillations, the two fluxes come into balance such that Ca²⁺ uptake by the stores during the ISI matches the amount released during the preceding spike. The time-dependent nucleation rate Λ(t) reaches only 60% of λ during an average ISI due to the small value of ξ. However, since the asymptotic nucleation rate λ is rather large, the oscillations in HEK cells have smaller σ than astrocyte oscillations. The values for λ and ξ of PLA cells lie between those for astrocytes and HEK cells.

We can further examine the stochastic component of wave triggering by manipulating the probability of wave initiation, for example by increasing the Ca²⁺-buffering capacity of the cytosol (10,11). Decreasing P_trig increases the average ISI, but if wave triggering is random, the standard deviation σ should also increase. P_trig is actually the probability of two sequential events: that a puff occurs (P_puff) and then that the puff ignites a wave (P_wave). The latter turns the puff frequency into the smaller wave frequency (P_trig = P_puffP_wave) and the standard deviation of interpuff intervals into the standard deviation of interspike intervals. P_wave is expected to decrease when diffusion of free Ca²⁺ between clusters (the spatial coupling) is reduced by buffers (11). The precise effect depends on the dynamic regime of the cell. With slow irregular waves, a slight decrease in coupling is predicted to increase T_av and σ, while larger decreases are predicted to abolish the self-amplifying mechanism required for oscillations leaving only moderate puff activity (10,11). Oscillations are predicted to be very sensitive to addition of Ca²⁺ buffers with fast binding and dissociation rates, and with similar to resting cytosolic Ca²⁺ concentration because such buffers effectively reduce diffusion of free Ca²⁺ at distances similar to the likely spacings of IP₃R clusters (11). Because the buffers we use do not change the resting cytosolic free Ca²⁺ concentration, the IP₃ concentration, or the interactions between IP₃Rs within clusters (41), we do not expect them to affect P_puff.

We measured the effect of Ca²⁺-buffering on oscillations in astrocytes, HEK cells, and PLA cells. Oscillations were first recorded to establish T_av and σ. The buffering capacity of the cells was then increased by incubating the cells with BAPTA-AM or EGTA-AM, before continuing measurements of [Ca²⁺]_i. BAPTA loading caused most of the HEK cells to stop oscillating, and for the cells that resumed oscillations (∼50% for cells loaded with 0.5 or 1 M BAPTA-AM), T_av and σ were both increased in a concentration-dependent way (Fig. 6, D–F). EGTA loading of PLA cells and astrocytes also caused oscillations to terminate in ∼80% of cells, and increased both T_av and σ in the cells that resumed oscillations (Fig. 6, A–C, G–I).

FIGURE 6.

Ca²⁺ buffers render spike times even less predictable. Results show Ca²⁺ spikes in astrocytes (A–C), HEK cells stimulated with 30 μM CCh (D–F), and PLA cells (G–I) before (red) and after (blue) loading with additional Ca²⁺ buffer. The protocols and typical results are shown in panels A, D, and G; the durations of the loading and subsequent hydrolysis times are shown in the triangles. Changes to concentrations of EGTA-AM or BAPTA-AM are shown in the histograms. For the 50% of cells that resumed Ca²⁺ spiking, changes dT_av and dσ in T_av and σ are shown relative to the values obtained before incubation with the Ca²⁺ buffer. Error bars show standard error from different cells and experiments.

The results demonstrate both the exquisite sensitivity of Ca²⁺ oscillations to Ca²⁺ buffering, whether provided by fast (BAPTA) or slow (EGTA) Ca²⁺ buffers, and the increase in both T_av and σ predicted for a stochastic mechanism dependent on repetitive Ca²⁺ waves (10).

We have shown that cells use a stochastic mechanism to generate global Ca²⁺ spikes. With ∼10⁴ IP₃Rs in each HEK cell (unpublished) and far more Ca²⁺ ions, why does random behavior play such an important part in Ca²⁺ spiking? The reason is that, as for any stochastic medium, global events are initiated by local processes. A puff changes the local free Ca²⁺ concentration by 100–1000-fold (11) and the gradients are so steep that only neighboring IP₃R clusters experience the change. Each puff, occurring within only a small part of the cell, is a potential wave initiation site, and the few IP₃R clusters that participate in the initiation of each wave are too few for the process to become deterministic. These properties identify intracellular Ca²⁺ dynamics as a random medium. The existence of so-called hot-spots (5) does not change these conclusions; it simply means that P_puff is not spatially homogeneous.

Intracellular Ca²⁺ spikes occur randomly. But a regular regime exists if P_trig is high due to the existence of a deterministic part of the ISI. The mean and the standard deviation of the ISI distribution depend on spatial coupling. The regular Ca²⁺ spikes are thus an example of array enhanced coherence resonance, an intrinsically stochastic phenomenon (10,13,15,16,42). This is consistent with hierarchical recruitment of Ca²⁺ release events (6,7). Hence, oscillations are an emergent property of arrays of IP₃R clusters and not a property of single IP₃Rs. Ca²⁺ oscillations are the first example of the constructive use of noise in cell signaling and the first experimental verification of AECR in a natural system.

These conclusions are based on the data presented here, previous measurements on the initiation of spikes and waves (6,7,9,43) and on theoretical studies investigating the role of noise and spatial coupling for global signals (10,16,42,44,45). It is accepted that elemental events like Ca²⁺ puffs and sparks are random (3,30,31,46–53), but this has not previously been shown for global events. Indeed, and despite the observation that over a large area of the cytosol (8 μm × 8 μm) of a Xenopus oocyte σ increases with T_av (9), it has been assumed that global signals are deterministic (2).

The probability of initiating a wave (P_trig) is determined by local properties, such as channel state dynamics, numbers of channels in a cluster, release currents, and by diffusion of free Ca²⁺ between clusters. P_trig sets σ of the ISI distribution. Information on local properties, like the open probability in vivo, can thus, in principle, be obtained from the fluctuations of the global Ca²⁺ signal.

We have shown that in many different cell types IP₃-evoked Ca²⁺ spikes are caused by random wave nucleation with a regular regime arising from AECR. The randomness of spike trains does not prevent Ca²⁺ oscillations from transmitting information. As long as the ISI distribution of stimulated spike trains is sufficiently different from the ISI distribution of spontaneous spiking (40), cells can distinguish the message from the noise.

SUPPLEMENTARY MATERIAL

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